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Voyager is passing through Devore space, where telepathy is illegal and telepaths are sent to relocation centers. Devore warships are far larger and more powerful than Voyager, so the ship is subject to frequent and random inspections to check for telepaths, complete with rough treatment of the crew and their equipment. Knowing the drill, Voyager and its crew are once again standing by to be boarded by Devore inspection teams and CaptainKathryn Janeway asks everyone to give them their full cooperation.

The lead Devore inspector Kashyk takes up residence in Captain Janeway's ready room. He plays the second movement of Mahler's First Symphony throughout the ship to "relax" the crew. He even replicates Janeway some coffee and asks her to make herself "at home".

Throughout the ship the crew has to endure humiliation at the hands of the Devore inspectors who are more than disrespectful. In Janeway's ready room, Kashyk expresses an interest in Human culture. He also allows Voyager to get away with two course deviations that his assistant, Prax, says would normally result in the ship being impounded, their crews detained and relocated. Kashyk says to the Captain that he is a reasonable man and given their long journey home, she certainly could use a friend like him. The Devore ships then leave Voyager, after which Captain Janeway orders that twelve Brenarirefugees, along with Tuvok, Jarot and Vorik, all of whom are telepathic, be brought out of transporter suspension in cargo bay one, which contains contaminated antimatter to block Devore sensors.

Janeway informs the passengers that the transport ship to pick them up is near. The Doctor and Tuvok also inform her of a bigger problem: due to being placed in transporter suspension so frequently, some have shown evidence of cell degradation. While trying to find a way out of their dilemma, Voyager suddenly detects a Devore vessel. Believing that yet another inspection is in order, Janeway orders all telepaths to go into transporter suspension again. However, it turns out that this ship is piloted by one man alone: Kashyk.
He is out of uniform and tells Janeway that he knows all about the telepathic refugees and that the nebula containing a wormhole that she plans to transport them to for their escape is a Devore trap. He says that he is defecting and requests asylum on the ship in return for his assistance in avoiding Devore ships. He assures her that he is her only way out of Devore space as only he knows about the ambush.

She agrees to grant him safe passage out of Devore space if the Brenari are amenable. The Brenari leader, Kir, agrees to cooperate. Kir points Janeway to a scientist, Torat, who can help them predict the next appearance of the wormhole. At this point, Janeway begins to cooperate with Kashyk. Torat is reluctant to help Voyager, so she introduces Kashyk as a fellow professor who doubts his work. To prove himself, and in exchange for mercurium isochromate, Torat provides the two with some data on the wormhole.

Later, Janeway and Kashyk work to pinpoint the next appearance of the wormhole. They simply do not seem to be able to predict a random occurrence. After standard algorithms fail, Janeway, considering the music that is playing in the background, the second movement of Tchaikovsky's Symphony Number Four, suggests that the pattern may be found in a subspace counterpoint: if they could run an algorithm based on subspace harmonics, they could reveal the pattern. Following this approach, the computer analysis finally works, allowing the next occurrence of the wormhole to be predicted.

Kashyk and Janeway also get into a discussion about their homeworlds and principles and guiding philosophies when Janeway notes that Kashyk is taking considerable risk defecting from his own people and assisting these telepaths. She asks him why and Kashyk explains that three months ago when his team was inspecting a plasma refining vessel, they found a family of telepaths hiding in one of the extraction tanks. There was a child – very young – who had been inside it for days, barely able to breathe. When he lifted her out of the tank and sat her on the deck, she thanked him. He then sent her to the relocation center with the others knowing full well what would happen to her. After that, he could think of nothing else. And when he couldn't stand it any longer, he decided to leave. He tells Janeway that she is his deliverance. While finishing telling his story, they are interrupted by the computer voice that informs them that the analysis is complete.

Janeway accompanies Kashyk back to his quarters who asks her to join him especially because he has been looking forward to trying their replicator. But Janeway tells him that this won't be possible as she had the replicator taken offline in case he decided to replicate a weapon. She wishes him a good night and leaves.

Unfortunately, Voyager is soon detected by a Devore scanning array again. Janeway plans to fight the ships with the new information about them she has obtained from Kashyk. But he tells her she will never survive against two of them and offers to take command of the impending inspection to ensure the refugees remain undetected. She is reluctant but still agrees. Right before his departure, they kiss passionately in the shuttle bay.

The Devore inspectors soon board the ship. Janeway meets Kashyk in her ready room, who plays the second movement of Tchaikovsky's Fourth Symphony and demands that she cease altering her course and leave Devore space. After sending Prax away, he asks about the wormhole. She tells him it is 20,000 kilometers off the portbow and that a photon torpedo properly calibrated will force open the threshold long enough for Voyager to get through. Kashyk congratulates her, ordering Prax to Cargo Bay One to capture the refugees and ordering two photon torpedoes to be fired to destroy the wormhole. Janeway, who finally recognizes the deception, tells him that he has given a masterful performance. Kashyk says that on the contrary, he is impressed with her selflessness and Humanity that made all this so much easier. She asks him whether his touching story about the little girl was a fabrication as well. He tells her that the story was real but what he didn't tell her was that after wrestling with his ethics he realized that he had done the right thing in order to protect his people from a very real threat. With armed guards he escorts her to the bridge and fires the torpedoes onto the wormhole to destroy it.

However, he soon realizes that it is he who has been double crossed: the neutrino emissions indicating a wormhole off the port bow are actually antimatter residue signatures, and it is not refugees, but cargo containers filled with vegetables that are suspended in the transporters in cargo bay one. Janeway changes the music to the second movement of Mahler's first symphony, while the refugees escape through the wormhole via shuttlecraft. Prax suggests that Voyager be impounded and the crew sent to detention centers, but Kashyk angrily notes that neither of them can benefit from having this failure on their records.

When they are alone on the bridge, Kashyk congratulates Janeway for having played this so well. She tells him that she had to take some precautions but that she never lied to him because her offer to take him with them was genuine, and it would still stand if he had kept his part of the bargain. Kashyk merely smiles at her and before leaving tells her that for what it was worth, she made a tempting offer.

Captain's log, supplemental. After weeks of playing hide and seek with the Devore inspectors, our goal is near: a transport vessel that will take our passengers to a wormhole leading out of hostile territory.

Captain's log, supplemental. It's taken us nearly two days but we've managed to locate Torat, the man who's supposedly an expert on wormholes. Unfortunately, he seems reluctant to share his expertise.

The original pitch for this episode – written by Gregory L. Norris and Laura Van Vleet, based on a screenplay of Van Vleet's, and entitled "The Hiding" – was focused on Seven of Nine. The refugees were hiding in Voyager's landing struts and, when Voyager was forced to land, Seven risked her life to take the refugees into neutral space in a shuttlecraft, against Janeway's orders. The two pitchers were delighted with the changes made to their pitch by Michael Taylor, in particular the focus on a love story for Janeway. (Star Trek Monthly issue 80) Janeway's romantic stirrings, however, were originally to have been with someone quite different from Kashyk. "The original 'love interest' was one of the people who were being victimized," offered Joe Menosky. "We just turned it on its head." (Cinefantastique, Vol. 31, No. 11, p. 41)

Story editor Nick Sagan was involved in the pitching of the original plot concept, which he referred to as "one of the pitches I took for Voyager." He went on to say, "The writers pitched it to me as this story about aliens hiding on Voyager. The big part I think [was] trying to find the hook of it, so I pitched it to [executive producer] Brannon [Braga] as 'The Diary of Anne Frank on Voyager'. I could see at least six different ways of that playing out, and I think creating those tantalizing possibilities is a huge part of pitching for Star Trek." [1]

According to the unofficial reference bookDelta Quadrant (p. 277), this installment – although containing only supplemental log entries – originally included a main entry that was ultimately cut for time.

Both Kate Mulgrew and Michael Taylor were of the opinion that this point in the series seemed a fitting time for Janeway to have a romantic liaison. Taylor offered, "It's about time Janeway had a romance, and a romantic partner worthy of her [....] [Kate Mulgrew] had been asking for some sort of romance, and when it came along, she saw that it was right for her character." (Cinefantastique, Vol. 31, No. 11, p. 38) Mulgrew herself commented of the episode, "This was, at long last, a story about the woman under the scientist." (Star Trek: Fan Collective - Captain's Log)

Kate Mulgrew thoroughly enjoyed this installment. She emotively described the outing as "a terrific episode" and said about the uncertainty of the motivations driving Janeway and Kashyk, "That was wonderful." The actress also enthused, "All of those layers, and all of those nuances and subtleties were terrific to play." (VOY Season 5 DVD easter egg) Additionally, Mulgrew remarked, "Well, I loved 'Counterpoint' [...] because I was so gratified, creatively [....] This was espionage at its best [....] It was a symphony, every scene with Mark Harelik [....] The whole marriage [between the writing, the characters and the actors] was almost perfect. I ran to work, every morning. So sorry when it ended. Every part was wonderful. Deeply satisfying work and that, you know, is everything." (Star Trek: Fan Collective - Captain's Log) In an interview shortly after filming, Mulgrew called this her "favorite episode to date." (citation needed • edit) In another, she claimed to have kissed the script when she first read it. (citation needed • edit) Subsequently, she chose it as her favorite episode, and it was included as such in Star Trek: Fan Collective - Captain's Log.

Michael Taylor was impressed by Kate Mulgrew's acting in this installment. Taylor commented, "I think it was a great chance for Kate to show what she can do [....] She played the role to the hilt." (Cinefantastique, Vol. 31, No. 11, p. 38)

According to the book Delta Quadrant (p. 276), the Devore firearms were reused rifles from the fourth season installment "Waking Moments".

Janeway's list of telepaths on Voyager includes only Tuvok, Vorik, Jarot, and Lon Suder. This confirms that Tuvok and Vorik are the only Vulcans aboard, although Janeway does mention that there are Vulcans (plural) other than Tuvok aboard in VOY: "Endgame" which appears to be a continuity error on that episode's part. Lt. Stadi, the Betazoid helmsman who is killed in Voyager's pilot episode, "Caretaker", and Kes, who was a crewmember until "The Gift", are also not listed here.

The whereabouts of the three telepathic crew members (Tuvok included) are not discussed at the end of the episode, although Tuvok is at his station on the Bridge when the inspection teams arrive.

This episode was selected by public vote in the UK as the best of the "Captain's Picks" (episodes selected by the four series' leads as their favorites) during the BBC's Star Trek Night on 16 September2001.

Joe Menosky was delighted with the writing of this episode and the change of Janeway's romantic interest to Kashyk. "How much interesting, if the 'romantic sparks' are between two enemies," Menosky commented. "It was one of those shows where you finish with the break and you just think, this is going to be great. This is where we found out what a good writer [Michael] Taylor is." (Cinefantastique, Vol. 31, No. 11, p. 41)